Montecito was among a number of towns and cities placed under evacuation orders on Monday.
The town in Santa Barbara County is about 148km north-west of Los Angeles and is home to other celebrities including the Kardashians.
The area has recorded more than 20cm of rain in the past 12 hours and was forecast to be hit by an additional 20cm into Tuesday, Montecito Fire Chief Kevin Taylor said.
Officials had placed Montecito under a shelter-in-place order on Monday morning but upgraded it to an evacuation order as the weather worsened.
Residents of Los Angeles County were advised to gather their pets, important information and other necessities in the event of an evacuation order.
More than 100,000 customers in the state were without power on Monday, according to power tracker PowerOutage.
The National Weather Service warned of a series of “atmospheric rivers” — storms that dump a significant amount of rainfall that could cause mudslides and flash flooding. Similar storms last week cut off power and inundated streets.
President Joe Biden on Sunday night approved an emergency declaration for the state that would provide federal assistance for disaster relief efforts.
Montecito deadly flood in 2018 — in pictures
California Governor Gavin Newsom said 12 people had died due to the violent weather in the past 10 days and warned the coming storm could become more dangerous.
Monday marked the fifth anniversary of a mudslide that killed 23 people and destroyed more than 100 homes in Montecito.
The Duke and Duchess of Sussex moved into their $14.6 million, 18,000-square-foot home in August 2020.
In an interview with ITV to promote his book Spare, Prince Harry said he and his family had left the UK for California “fearing for our lives”, as they left royal life behind.
The couple's Archewell Foundation did not immediately return The National's request for comment.